Opdracht 9b ----------- t-procedures for a single sample In 1798 the English scholar Henry Cavendish measured the density of the earth with a torsion balance. The observed variable was the density of the earth as a multiple of the density of water. Cavendish's measurements are below (source: S. M. Stigler, 'Do robust estimators work with real data?', Annals of Statistics, 5 (1977), pp. 1055-1078.) 5.50 5.61 4.88 5.07 5.26 5.55 5.36 5.29 5.58 5.65 5.57 5.53 5.62 5.29 5.44 5.34 5.79 5.10 5.27 5.39 5.42 5.47 5.63 5.34 5.46 5.30 5.75 5.68 5.85 The sample mean x_mean=5.45 and the sample standard deviation is s=0.22. The data are in z:\public\share\heeringa\dicht.txt. Read this ASCII- file in. Define the column and choose a good variable name. a. Draw a histogram for these measurements and combine it with a normal curve. b. Determine the 99% confidence interval. c. Suppose that current measurements showed that the true density of the earth is 6.1 Are Cavendish's results then significantly different from the value determined currently? Formulate the appropriate H_0 and H_a.